Re: set of a set etc.

On Tue, 19 Jul 2005 14:24:15 -0700, William Elliot
<marsh@xxxxxxxxxxxxxxxxxx> wrote:

> On Tue, 19 Jul 2005, G. Frege wrote:
>
> > "The distinction between x and {x} is one of the merits of Peano's
> > symbolic logic, as well as Frege's. On the basis of our theory of
> > classes, the necessity for the distinction is of course obvious. But
> > apart from this, the following consideration makes the necessity
> > apparent. Let /a/ be a class; then the class whose only member is /a/
> > has only one member, namely /a/, while /a/ may have many members. Hence
> > the class whose only member is /a/ cannot be identical with /a/."
> >
> The difference between a, {a}, {{a}} and {{{a}}} is[:] a is something[,]
> {a} is a in a box, {{a}} is a in a box within a box and {{{a}}} is a in
> a box within a box within yet another box and etc for so on.
>
Indeed, almost the same comment can be found in Halmos' famous book
"Naive Set Theory", though I can't tell you which page, since I don't
own the English version of the book. (Hint: it should be on the first
page of Chapter 2.)


F.

.

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